Hover or tap a manifold on the compass — or drag the slider below to test the conjecture at any angle.
Conjecture tester
Pick any angle θ* and see what the Eisenstein conjecture predicts for the trace field.
θ* = −180.0°
Six arithmetic 3-manifolds with H₁ = ℤ/5. Two confirm the Eisenstein conjecture exactly (m003, m004).
m006 and m038 correctly refute it. m206(1,2) is a near-miss: θ* = −59.02°, only 0.98° from −60°,
yet its trace field (disc = −23) shares no factor with 3. m032 remains open (degree-6 field).
The slot at +60° is a standing prediction — no known manifold occupies it yet.